I learned the material from a course that used Lee but used Tu as a reference for qualifying exams and also as a reference since then. Tu's book really is the best to get into the subject quickly and concisely, particularly someone without a course in topology. This means that he develops the material on $\mathbb^n$ first, and then uses these results plus minimal topology to generalize to manifolds. The reason is that he specifically delays the need for topology so as to get into the meat of the subject quicker. I highly recommend Introduction to Manifolds by Loring Tu. However, as I have very limited knowledge about the differential geometry, I am not sure whether this would be good starting point.Ĭan someone suggest me a good reference (and prerequisites, if necessary,for studying above topics)? Thanks in Advance. As I am not from math major, I am confused over many previous questions asking suggestions for differential geometry, such as this, this, this, and many other answers on the similar questions.įrom search on good books on the topic, I found out O'neill's Elementary Differential Geometry is meant for first course on the differential geometry. I am looking to learn topics such as Lie derivative, covarient-contravarient derivatives, pushforward pullback operations, Riemannian manifolds, moving frames, etc. I have background of linear algebra and advanced calculus. At starting point, I am not looking for a comprehensive book (may be Spivak's Comprehensive Introduction to Differential Geometry series). I am an engineering major and looking for a straightforward, easy to understand basic book on differential geometry to get started.
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